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Average Velocity and Acceleration
Where it all began For hundreds and hundreds of years, we have tried to explain the phenomenon that is our world. We have applied abstract thought to give reason to why everything happens. To discover how fast objects moved in earth (and eventually space!), people have coined the term velocity. However, this is only one piece of basic motion, we also wanted to know how velocity was changing over time, hence acceleration was brought into the picture. Average velocity and acceleration were used for centuries to describe motion, but how objects acted at an instant was still considered unattainable. This question remained unanswered until the late 1600s where the credit for the invention of calculus is usually given to Sir Isaac Newton. The tangent line problem which depicts instanteous rate was then applied to enhance the study of motion. However for simplistic terms, we'll only focus on v = d/t and a = delta(v)/t. ---- Those famous people who probably stood on each other's shoulders It is impossible to find who originally discovered the main ideas that we use today for motion. Going back to the Ancient Greeks, there is evidence to show that they had a profound understanding of basic motion and even evidence of integrals (Calculus). However, it took many centuries before one man correctly interpreted how objects prefer to stay in uniform motion. The credit of understanding how this motion works is given to Isaac Newton. Born in the Early 17th century, Newton contributed much to the mathematical and scientific department. His works involve forces, which affect acceleration and velocity as well as linear motion (inertia) and equal but opposite forces (constant velocity). ---- Average Velocity Average Velocity is defined to be displacement/time where displacement is distance from the original starting position. This leads us to another small bit of necessary information, velocity unlike speed is a vector not a scalar. A vector is identical except it has a direction associated with it, here in the equation v = d/t, t is not a vector because time only has one direction; displacement however can be north, west, south, left, right, up or down and therefore is a vector. This by definiton also makes velocity a vector. We use velocity to help us find out how long it takes for storms to reach the coastline, rockets to get to the moon and many other applications. ---- Average Acceleration Well we can easily find how fast one person goes by just finding out their distance from a starting point and how long it took them to get to their new location, but what happens if they start out slow and begin to uniformly increase their velocity? How would we find how fast their rate of change is changing? To find this, we are actually looking for the acceleration of an object (deceleration is an unnecessary term for an object slowing down, we can simply use a negative sign because acceleration is a vector, which means it has a direction). The acceleration of an object is the objects change in velocity divided by the time interval in which it is changing. ---- Some Useful Formulas v = d/t a = (vf-vi)/t v(of two rates) = 2v1v2/(v1+v2) vf^2 = vi^2 + 2ad d = (vi)t + 0.5at^2 vi = initial velocity vf = final velocity v = average velocity d = distance t = time a = acceleration ---- Regents Review 1. A Basketball player jumped straight up to catch a rebound and was in the air for .80 seconds, how high did she jump? 2. A car is driving down a rode at 20 m/s. If it suddenly turns on its brakes until rest over a distance of 10 m, what was the acceleration of the car? 3. A baseball is thrown upward at an initial velocity of 30 m/s, what is the max height reached? At what time does it reach this point? How long is the baseball in the air? ---- References Physics Textbook, "Principles and Problems" Zitzewitz